Condition (S+), introduced in [KT5], plays a key role in the study of Kloosterman and hypergeometric l-adic local systems in positive characteristic p. Prior results of [KT5], [KT8] establish (S+) for primitive Kloosterman and hypergeometric sheaves, except possibly in ranks 4, 8, and 9. In this paper we study (S+) in these remaining ranks, and completely determine when (S+) does or does not hold.
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Katz et al. (2024) studied this question.
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